Supplemental Materials For: Assessment of goose-beaked whale responses to mid-frequency active sonar using a hierarchical hidden Markov model
Supplemental Tables
Dive-cycle Summary
MFAS exposure details
Variant State Occurrence per MFAS-exposed Dive Cycle
Here, we see that whales transitioned to Variant state in 12 out of 52 MFAS-exposed dive cycles (23.1 percent).
If we consider only dive cycles where the MFAS cSEL was above 110 dB re 1\(\mu Pa^2*sec\), then that becomes 12 out of 40 MFAS-exposed dive cycles (30 percent).
MFAS Received Level Data Table
All received level values (for each received sound, as opposed to summarised over 5-minute or dive-cycle periods) are also available as text files.
File name: mfas-raw-rls.csv (located in the data directory).
Note: Each table printed above is also available as a text file in the data directory.
Tallying 5-Minute States
Duration of Variant State
Data Variant State Bouts
Variant State Summary
| Type | Metric | median | IQR | mean | sd | min | max |
|---|---|---|---|---|---|---|---|
| Observed | Dive Cycles | 2.0 | 3.0 | 3.8 | 5.4 | 1.0 | 37.0 |
| Observed | Duration (h) | 9.0 | 9.2 | 10.9 | 11.5 | 1.0 | 72.4 |
| Simulated | Dive Cycles | 3.0 | 4.0 | 3.6 | 3.3 | 1.0 | 29.0 |
| Simulated | Duration (h) | 7.5 | 10.7 | 10.7 | 10.5 | 0.3 | 109.6 |
Time-series plots for each tag deployment
Dive Profile Plots
Below are dive trace time-series plots for all whales with RLs and coarse-scale state indicated.
In these plots:
- Grey shading indicates a dive cycle that was classed as Variant state
- Received levels are shown in lower plots. The lines indicate cumulative SEL (cumulative by dive cycle; for the 5-minute scale, SEL is cumulative across a single dive cycle up to the end of the current 5-minute interval). Dots indicate RMS RL.
- Depths shown are the medians in 5-minute intervals (so may not reach the surface, etc.)
- Colors indicate the fine-scale (5-minute) states
- In interactive plots (in html output file format),
- You can zoom!
- Mouse over the RL dot to get the exact RL value
Dive Cycle Plots
Below are time-series plots for each whale, showing dive-cycle-scale observations (with “dive cycle number” on x axis). MFAS levels and coarse-scale state (decoded using the fitted HHMM and the Viterbi algorithm) are also indicated.
Variant Timecourse
We can also consider dive-cycle characteristics of variant dive cycles as a function of dive-cycle number within the sequence of several variant dive cycles. This could help investigate the question of whether there might be differences between “initial” and “later” variant behavior.
Depth Distribution of 5-minute States
HHMM Model Validation & Interpretation
Stationary Distributions
Based on the transition probability matrices, we can compute stationary distributions based on the model, which present the proportion of “time” whales would be expected to spend in each state in the long run. (“Time” because it’s the proportion of time-steps, which for the coarse dive-cycle states is not exactly the same as the duration of dive cycles varies.)
Lag plots
These plots may sometimes help verify the number of states in the data, as discussed in Lawler et al. 2019 and Sidrow et al. 2022
Model Pseudoresiduals
Computing pseudo-residuals...
Likelihood Weighting Simulation Results
Case 1: True Model Includes MFAS Effect
AIC and likelihood results
| Weighting? | Proportion dAIC > 6 |
|---|---|
| No | 0.81 |
| Yes | 1.00 |
Confidence Interval Coverage
| Model Name | N Simulations | CI Coverage (%; P(T->V)) | CI Coverage (%; P(V->T)) | Mean Absolute Error (%; P(T->V)) | Mean Absolute Error (%; P(V->T)) |
|---|---|---|---|---|---|
| rl_coarse | 101 | 96.0 | 43.10 | 30.6 | 290 |
| rl_coarse_wt | 101 | 26.7 | 8.54 | 32.1 | 421 |
Power
Based on CIs, how often would we conclude there IS an MFAS effect (when there really is)?
| Model Name | Power (%, P(T->V)) | Power (%, P(V->T)) |
|---|---|---|
| rl_coarse | 75.2 | 32.3 |
| rl_coarse_wt | 99.0 | 100.0 |
Case 2: True Model Excludes MFAS Effect
AIC and likelihood results
| Weighting? | Proportion dAIC > 6 |
|---|---|
| No | 0.008849558 |
| Yes | 0.882882883 |
Confidence Interval Coverage
| Model Name | N Simulations | CI Coverage (%; P(T->V)) | CI Coverage (%; P(V->T)) |
|---|---|---|---|
| rl_coarse | 113 | 97.3 | 96.4 |
| rl_coarse_wt | 112 | 25.9 | 19.6 |